define absolutely equicontious integral
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INTRODUCTION. In this note we prove that an equicontinuous family of finitely additive Banach-valued measures, each absolutely continuous with respect to a fixed finitely additive measure h, is uniformly absolutely continuous with respect to h (Theorem 1). The domain of definition can be chosen to be a ring of sets.
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In this note we prove that an equicontinuous family of finitely additive Banach-valued measures, each absolutely continuous with respect to a fixed finitely additive measure h, is uniformly absolutely continuous with respect to h (Theorem 1). The domain of definition can be chosen to be a ring of sets.
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